1
var('x')
x x |
taylor(exp(x), x, 0, 8)
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taylor(sin(x), x, 0, 8)
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taylor(cos(x), x, 0, 8)
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Grafieken
( plot(exp(x), (x, -3,3), color='red', legend_label='cos(x)')
+ sum(
plot(taylor(exp(x), x, 0, i),
(x, -3, 3),
color=hue(pi*(2+i)),
legend_label='taylor %d'%i)
for i in [0, 1, 2, 3])
).show(ymin=-2, ymax=5)
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2
( plot(cos(x), (x, -10,10), color='red', legend_label='cos(x)')
+ sum(
plot(taylor(cos(x), x, 0, i),
(x, -10, 10),
color=hue(pi*i),
legend_label='taylor %d'%i)
for i in range(2,20,2))
).show(ymin=-10, ymax=10)
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( plot(log(x), (x, -1,3), color='red', legend_label='cos(x)')
+ sum(
plot(taylor(log(x), x, 1, i),
(x, -1, 3),
color=hue(golden_ratio*i),
legend_label='taylor %d'%i)
for i in range(2,50,7))
).show(ymin=-5, ymax=3)
verbose 0 (3744: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 51 points. verbose 0 (3744: plot.py, generate_plot_points) Last error message: 'can't convert complex to float' verbose 0 (3744: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 51 points. verbose 0 (3744: plot.py, generate_plot_points) Last error message: 'can't convert complex to float' 
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3
f(x) = 1./(1-x) - 1./(1+x)
g(x) = taylor(f, x, 0, 10)
plot(f, (-.9,.9), color='red', legend_label='f(x)') + plot(g, (-.9,.9), color='blue', legend_label='g(x)')
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plot(f, (-1e-15,1e-15), color='red', legend_label='f(x)') + plot(g, (-1e-15,1e-15), color='blue', legend_label='g(x)')
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4
eps = RDF.epsilon()
f = lambda x: tan(x)
hs = map(RDF, [10^-k for k in range(17)])
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x = RDF(1)
list_plot_loglog([(h, abs((f(x+h) - f(x))/h - 1/cos(x)^2)) for h in hs])
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